Calibration Methods and Progress for Internal and External Parameters of Area-Array Camera

Yanqing Shi; Caixia Chang; Xiaohong Liu; Ziyu Li; Zonghua Zhang; Nan Gao; Zhaozong Meng

doi:10.3788/LOP202158.2400001

[1] Marrugo A G, Gao F, Zhang S. State-of-the-art active optical techniques for three-dimensional surface metrology: a review[J]. Journal of the Optical Society of America A, 37, B60-B77(2020).

[2] Wang Z Z. Review of real-time three-dimensional shape measurement techniques[J]. Measurement, 156, 107624(2020).

[3] Ma Y Z, Tao L Y, Wang X H. Application of computer vision technology[J]. Test Technology and Testing Machine, 46, 60-65(2006).

[4] Gao X, Zhang T. Robust RGB-D simultaneous localization and mapping using planar point features[J]. Robotics and Autonomous Systems, 72, 1-14(2015).

[5] Xu J, Zhang S. Status, challenges, and future perspectives of fringe projection profilometry[J]. Optics and Lasers in Engineering, 135, 106193(2020).

[6] Guo W B, Zhang Q C, Wu Z J. Real-time three-dimensional imaging technique based on phase-shift fringe analysis: a review[J]. Laser & Optoelectronics Progress, 58, 0800001(2021).

[7] Pavlidis G, Koutsoudis A, Arnaoutoglou F et al. Methods for 3D digitization of cultural heritage[J]. Journal of Cultural Heritage, 8, 93-98(2007).

[8] Wang W G, Hu Z Y, Shun Z Y. 3D shape measurement based on computer vision[C]. //Proceedings of International Conference on Machine Learning and Cybernetics, November 4-5, 2002, Beijing, China., 910-914(2002).

[9] Baqersad J, Poozesh P, Niezrecki C et al. Photogrammetry and optical methods in structural dynamics: a review[J]. Mechanical Systems and Signal Processing, 86, 17-34(2017).

[10] Do P N B, Nguyen Q C. A review of stereo-photogrammetry method for 3-D reconstruction in computer vision[C]. //2019 19th International Symposium on Communications and Information Technologies (ISCIT), September 25-27, 2019, Ho Chi Minh City, Vietnam., 138-143(2019).

[11] Zhang D H, Liang J, Guo C. Comparison method for CCD camera accuracy in photography measurement[J]. Journal of Applied Optics, 30, 279(2009).

[12] Sims-Waterhouse D, Piano S, Leach R. Verification of micro-scale photogrammetry for smooth three-dimensional object measurement[J]. Measurement Science and Technology, 28, 055010(2017).

[13] Atkinson K B, Newton I. The photogrammetric society: 1952--2001[J]. The Photogrammetric Record, 17, 577-600(2002).

[14] Poulin-Girard A S, Thibault S, Laurendeau D. Influence of camera calibration conditions on the accuracy of 3D reconstruction[J]. Optics Express, 24, 2678-2686(2016).

[15] Chang C X, Zhang Z H, Gao N et al. Improved infrared phase measuring deflectometry method for the measurement of discontinuous specular objects[J]. Optics and Lasers in Engineering, 134, 106194(2020).

[16] Wong K Y K, Mendonca P R S, Cipolla R. Camera calibration from surfaces of revolution[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25, 147-161(2003).

[17] Hu G Y, He P A, Wang B L et al. Overview of camera calibration in visual measurement[J]. Optics & Optoelectronic Technology, 2, 9-12(2004).

[18] Guo Y, Yang H, Yang Z J et al. Distortion measurement of lens in CCD camera system[J]. Journal of Applied Optics, 29, 279-282(2008).

[19] Song L M, Wang M P, Lu L et al. High precision camera calibration in vision measurement[J]. Optics & Laser Technology, 39, 1413-1420(2007).

[20] Orteu J J, Garric V, Devy M. Camera calibration for 3D reconstruction: application to the measurement of 3D deformations on sheet metal parts[J]. Proceedings of SPIE, 3101, 252-263(1997).

[21] Sun Q, Wang X Y, Xu J P et al. Camera self-calibration with lens distortion[J]. Optik, 127, 4506-4513(2016).

[22] Gao X, Zhang T, Liu Y. Visual SLAM fourteen lectures: from theory to practice[M], 97-104(2017).

[23] Hartley R, Zisserman A. Multiple view geometry in computer vision[M](2004).

[24] Zhang G J. Vision measurement[M](2008).

[25] Juarez-Salazar R, Zheng J, Diaz-Ramirez V H. Distorted pinhole camera modeling and calibration[J]. Applied Optics, 59, 11310-11318(2020).

[26] Evagorou E, Mettas C, Agapiou A et al. Digital camera calibration for cultural heritage documentation: the case study of a mass digitization project of religious monuments in Cyprus[J]. European Journal of Remote Sensing, 54, 6-17(2021).

[27] Ghosh P K, Mudur S P. Three-dimensional computer vision: a geometric viewpoint[J]. The Computer Journal, 38, 85-86(1995).

[28] Zhang Z Y. A flexible new technique for camera calibration[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 1330-1334(2000).

[29] He H, Li H Y, Huang Y B et al. A novel efficient camera calibration approach based on K-SVD sparse dictionary learning[J]. Measurement, 159, 107798(2020).

[30] Heikkila J, Silven O. A four-step camera calibration procedure with implicit image correction[C]. //Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 17-19, 1997, San Juan, PR, USA., 1106-1112(1997).

[31] Kim J S, Gurdjos P, Kweon I S. Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 637-642(2005).

[32] He D, Liu X L, Peng X et al. Eccentricity error identification and compensation for high-accuracy 3D optical measurement[J]. Measurement Science & Technology, 24, 075402(2013).

[33] An J J, Gao N, Chen C et al. Correcting method and evaluation of eccentricity error of circle target[J]. Laser & Optoelectronics Progress, 54, 041203(2017).

[34] Schmalz C, Forster F, Angelopoulou E. Camera calibration: active versus passive targets[J]. Optical Engineering, 50, 113601(2011).

[35] Abdel-Aziz Y I, Karara H M, Hauck M. Direct linear transformation from comparator coordinates into object space coordinates in close-range photogrammetry[J]. Photogrammetric Engineering & Remote Sensing, 81, 103-107(2015).

[36] Yakimovsky Y, Cunningham R. A system for extracting three-dimensional measurements from a stereo pair of TV cameras[J]. Computer Graphics and Image Processing, 7, 195-210(1978).

[37] Sun J, Wang P, Qin Z K et al. Overview of camera calibration for computer vision[C]. //Proceeding of the 11th World Congress on Intelligent Control and Automation, June 29-July 4, 2014, Shenyang, China., 86-92(2014).

[38] Ye F, Wang M, Chen J D et al. Camera nonlinear distortion correction based on coplanar points[J]. Optics and Precision Engineering, 23, 2962-2970(2015).

[39] Tsai R Y. A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses[J]. IEEE Journal on Robotics and Automation, 3, 323-344(1987).

[40] Zhang Z Y. Motion and structure from two perspective views: from essential parameters to Euclidean motion through the fundamental matrix[J]. Journal of the Optical Society of America A, 14, 2938-2950(1997).

[41] Sid-Ahmed M A, Boraie M T. Dual camera calibration for 3-D machine vision metrology[J]. IEEE Transactions on Instrumentation and Measurement, 39, 512-516(1990).

[42] Weng J, Cohen P, Herniou M. Calibration of stereo cameras using a non-linear distortion model (CCD sensory)[C]. //[1990] Proceedings. 10th International Conference on Pattern Recognition, June 16-21, 1990, Atlantic City, NJ, USA., 246-253(1990).

[43] Martins H A, Birk J R, Kelley R B. Camera models based on data from two calibration planes[J]. Computer Graphics and Image Processing, 17, 173-180(1981).

[44] Jiang G, Quan L. Detection of concentric circles for camera calibration[C]. //Tenth IEEE International Conference on Computer Vision (ICCV’05), October 17-21, 2005, Beijing, China., 333-340(2005).

[45] Zhang Z H, Wang S, Wang Y Y et al. Method for extracting the center of circular coded target based on radial straight line fitting of circular coding[J]. Laser & Optoelectronics Progress, 57, 071203(2020).

[46] Lu X D, Xue J P, Zhang Q C. High camera calibration method based on true coordinate computation of circle center[J]. Chinese Journal of Lasers, 47, 0304008(2020).

[47] Xue J P, Su X Y, Dou Y F. A concentric circles and wedge grating-based camera self-calibration method[J]. Chinese Journal of Lasers, 39, 0308002(2012).

[48] Huang L, Zhang Q C, Asundi A. Camera calibration with active phase target: improvement on feature detection and optimization[J]. Optics Letters, 38, 1446-1448(2013).

[49] Ma M C, Chen X C, Wang K Y. Camera calibration by using fringe patterns and 2D phase-difference pulse detection[J]. Optik, 125, 671-674(2014).

[50] Sagawa R, Takatsuji M, Echigo T et al. Calibration of lens distortion by structured-light scanning[C]. //2005 IEEE/RSJ International Conference on Intelligent Robots and Systems, August 2-6, 2005, Edmonton, AB, Canada., 832-837(2005).

[51] Liu Y K, Su X Y. Camera calibration with planar crossed fringe patterns[J]. Optik, 123, 171-175(2012).

[52] Große M. Camera calibration using time-coded planar patterns[J]. Optical Engineering, 51, 083604(2012).

[53] Xue J P, Su X Y, Xiang L Q et al. Using concentric circles and wedge grating for camera calibration[J]. Applied Optics, 51, 3811-3816(2012).

[54] Xu Y J, Gao F, Ren H Y et al. An iterative distortion compensation algorithm for camera calibration based on phase target[J]. Sensors, 17, 1188(2017).

[55] Yu J, Chen C, Gao N et al. Camera calibration based on phase target[J]. Laser & Optoelectronics Progress, 55, 111203(2018).

[56] Bell T, Xu J, Zhang S. Method for out-of-focus camera calibration[J]. Applied Optics, 55, 2346-2352(2016).

[57] Wang Y W, Chen X C, Tao J Y et al. Accurate feature detection for out-of-focus camera calibration[J]. Applied Optics, 55, 7964-7971(2016).

[58] Faugeras O D, Quan L, Strum P F. Self-calibration of a 1D projective camera and its application to the self-calibration of a 2D projective camera[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 1179-1185(2000).

[59] Pollefeys M, van Gool L. A stratified approach to metric self-calibration[C]. //Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 17-19, 1997, San Juan, PR, USA., 407-412(1997).

[60] Pollefeys M, Koch R, van Gool L. Self-calibration and metric reconstruction inspite of varying and unknown intrinsic camera parameters[J]. International Journal of Computer Vision, 32, 7-25(1999).

[61] Xu S, Sun XX, Liu X et al. Geometry method of camera self-calibration based on a rectangle[J]. Acta Optica Sinica, 34, 1115002(2014).

[62] Quan L. Self-calibration of an affine camera from multiple views[J]. International Journal of Computer Vision, 19, 93-105(1996).

[63] Faugeras O D, Luong Q T, Maybank S J. Camera self-calibration: theory and experiments[M]. //Sandini G. Computer vision-ECCV’92. Lecture notes in computer science, 588, 321-334(1992).

[64] Faugeras O D. What can be seen in three dimensions with an uncalibrated stereo rig?[M]. //Sandini G. Computer vision-ECCV’92. Lecture notes in computer science, 588, 563-578(1992).

[65] Maybank S J, Faugeras O D. A theory of self-calibration of a moving camera[J]. International Journal of Computer Vision, 8, 123-151(1992).

[66] Lei C, Wu F C, Hu Z Y. Kruppa equations and camera self-calibration[J]. Acta Automatica Sinica, 27, 621-630(2001).

[67] Jin J, Li X F. Efficient camera self-calibration method based on the absolute dual quadric[J]. Journal of the Optical Society of America A, 30, 287-292(2013).

[68] Golub G H, van Loan C F. Matrix computations[J]. The Mathematical Gazette, 47, 392-396(1996).

[69] Faugeras O D. Stratification of three-dimensional vision: projective, affine, and metric representations: errata[J]. Journal of the Optical Society of America A, 12, 1606(1995).

[70] Wang G H, Wu Q M J. Quasi-perspective projection model: theory and application to structure and motion factorization from uncalibrated image sequences[J]. International Journal of Computer Vision, 87, 213-234(2010).

[71] Zhang Z Y, Xu G. A unified theory of uncalibrated stereo for both perspective and affine cameras[J]. Journal of Mathematical Imaging and Vision, 9, 213-229(1998).

[72] Triggs B. Autocalibration and the absolute quadric[C]. //Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 17-19, San Juan, Puerto Rico., 604-614(1997).

[73] Zhu J, Li X F, Xu Y X. Camera calibration technique based on activevision[J]. Acta Optica Sinica, 30, 1297-1303(2010).

[74] Moons T, van Gool L, Proesmans M et al. Affine reconstruction from perspective image pairs with a relative object-camera translation in between[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, 77-83(1996).

[75] de Agapito L, Hartley R I, Hayman E. Linear self-calibration of a rotating and zooming camera[C]. //Proceedings of 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149), June 23-25, 1999, Fort Collins, CO, USA., 15-21(1999).

[76] Hartley R I. Self-calibration of stationary cameras[J]. International Journal of Computer Vision, 22, 5-23(1997).

[77] Ma S D. A self-calibration technique for active vision systems[J]. IEEE Transactions on Robotics and Automation, 12, 114-120(1996).

[78] Lei C, Wu F C, Hu Z Y. A new camera self-calibration method based on active vision system[J]. Chinese Journal of Computers, 23, 1130-1139(2000).

[79] Li H, Wu F C, Hu Z Y. A new linear camera self-calibration technique[J]. Chinese Journal of Computers, 23, 1121-1129(2000).

[80] Wu F C, Hu Z Y. A new theory and algorithm of linear cameraself calibration[J]. Chinese Journal of Computers, 24, 1221-1235(2001).

[81] Wu F C, Hu Z Y. Linear determination of the infinite homography and camera self-calibration[J]. Acta Automatica Sinica, 28, 488-496(2002).

[82] Li H, Hu Z Y. A linear camera self-calibration technique based on projective reconstruction[J]. Journal of Software, 13, 2286-2296(2002).

[83] Sun W, He X Y, Zheng X. Three-dimensional displacement measurement based on single CCD camera[J]. Acta Optica Sinica, 28, 1723-1729(2008).

[84] Gu G H, Wang J J, Chen Q et al. Camera parameter calibration based on two-dimensional rotating platform[J]. Optics and Precision Engineering, 25, 1890-1899(2017).

[85] Xu Q Y, Yang L H, Niu Z Y et al. High-accuracy calibration of multi-camera positioning system based on precision angle reference[J]. Acta Optica Sinica, 39, 0115001(2019).

[86] Cai P, Li X Y, Tang Y J et al. Improved distortion correction method for spacial large aperture tracking cameras[J]. Optics and Precision Engineering, 27, 2272-2279(2019).

[87] Yuan M, Su X Y, Liu X Q. Analysis of factors on the precision of the camera calibration[J]. Optics & Optoelectronic Technology, 8, 18-21(2010).

[88] Xu Q Y, Yao H, Che R S. Online calibration of stereo vision measurement system[J]. Acta Optica Sinica, 29, 1546-1551(2009).

[89] Sun J H, Wu Z Y, Liu Q Z et al. Field calibration of stereo vision sensor with large FOV[J]. Optics and Precision Engineering, 17, 633-640(2009).

[90] Chen H, Ye D, Che R S et al. Stereo camera calibration based on accurate control points[J]. Optics and Precision Engineering, 14, 903-909(2006).

[91] Ye D, Xu Q Y, Che R S. Camera calibration technique for vision measurement system[J]. Optics and Precision Engineering, 14, 883-890(2006).

[92] Ye D, Liu C Y, Che R S et al. Dummy solid camera calibration technology using genetic algorithm[J]. Optics and Precision Engineering, 14, 485-489(2006).

[93] Yang B W, Zhang L Y, Ye N et al. Camera calibration technique of wide-area vision measurement[J]. Acta Optica Sinica, 32, 0915001(2012).

[94] Yan A Q, Yang J F, Cao J Z et al. Optical system design of space fisheye camera[J]. Acta Optica Sinica, 31, 1022004(2011).

[95] Niu Z Q, Gao N, Zhang Z H et al. 3D shape measurement of discontinuous specular objects based on advanced PMD with bi-telecentric lens[J]. Optics Express, 26, 1615-1632(2018).

[96] Silvatti A P, Salve Dias F A, Cerveri P et al. Comparison of different camera calibration approaches for underwater applications[J]. Journal of Biomechanics, 45, 1112-1116(2012).

[97] Hu X W, Wang G J, Wang J N et al. A robust and accurate calibration method for out-of-focus camera[J]. Electronic Imaging, 2018, 1-5(2018).

[98] Liao H Y, Chen Z, Zhang X M. Calibration of camera with small FOV and DOF telecentric lens[C]. //2013 IEEE International Conference on Robotics and Biomimetics (ROBIO), December 12-14, 2013, Shenzhen, China., 498-503(2013).

[99] Lu L J, Liu M, Shi Y. Correction method of image distortion of fisheye lens[J]. Infrared and Laser Engineering, 48, 0926002(2019).

[100] Kim H, Kim D, Paik J et al. Automatic estimation of spatially varying focal length for correcting distortion in fisheye lens images[J]. IEIE Transactions on Smart Processing and Computing, 2, 339-344(2013).

[101] Schneider D, Schwalbe E, Maas H G. Validation of geometric models for fisheye lenses[J]. ISPRS Journal of Photogrammetry and Remote Sensing, 64, 259-266(2009).

[102] Obukhova N A, Motyko A A, Pozdeev A A. Research and development of methods for endoscopic (medical) images enhancement[J]. Journal of the Russian Universities Radioelectronics, 22-30(2019).

[103] Zhou W S, Weng J W, Peng J Z et al. Wide-angle lenses distortion calibration using phase demodulation of phase-shifting fringe-patterns[J]. Infrared and Laser Engineering, 49, 20200039(2020).

[104] Kakani V, Kim H, Kumbham M et al. Feasible self-calibration of larger field-of-view (FOV) camera sensors for the advanced driver-assistance system (ADAS)[J]. Sensors, 19, 3369(2019).

[105] Kim J S, Kanade T. Multiaperture telecentric lens for 3D reconstruction[J]. Optics Letters, 36, 1050-1052(2011).

[106] Li D, Tian J D. An accurate calibration method for a camera with telecentric lenses[J]. Optics and Lasers in Engineering, 51, 538-541(2013).

[107] Liu H B, Lin H J, Yao L S. Calibration method for projector-camera-based telecentric fringe projection profilometry system[J]. Optics Express, 25, 31492-31508(2017).

[108] Fryer J G, Fraser C S. On the calibration of underwater cameras[J]. The Photogrammetric Record, 12, 73-85(2006).

[109] Li S Q, Xie X P, Zhuang Y J. Research on the calibration technology of an underwater camera based on equivalent focal length[J]. Measurement, 122, 275-283(2018).

[110] Konovalenko I A, Sidorchuk D S, Zenkin G M. Analysis and compensation of geometric distortions, appearing when observing objects under water[J]. Pattern Recognition and Image Analysis, 28, 379-392(2018).

[111] Schettini R, Corchs S. Underwater image processing: state of the art of restoration and image enhancement methods[J]. EURASIP Journal on Advances in Signal Processing, 2010, 746052(2010).

[112] Zhao Y Q, Dai H M, Shen L H et al. Review of underwater polarization clear imaging methods[J]. Infrared and Laser Engineering, 49, 20190574(2020).

[113] Shortis M. Calibration techniques for accurate measurements by underwater camera systems[J]. Sensors, 15, 30810-30826(2015).

[114] Wu X J, Li H S. A simple and comprehensive model for underwater image restoration[C]. //2013 IEEE International Conference on Information and Automation (ICIA), August 26-28, 2013, Yinchuan, China., 699-704(2013).

[115] Guo T, Da F P, Fang X. Camera calibration under small field of view[J]. Chinese Journal of Lasers, 39, 0808001(2012).

[116] Yang H, Cai N, Lin B et al. Defocus camera calibration based on sinusoidal phase coding[J]. Acta Photonica Sinica, 47, 0715002(2018).

[117] An Y T, Bell T, Li B W et al. Method for large-range structured light system calibration[J]. Applied Optics, 55, 9563-9572(2016).

[118] Guo G D, Zhang N. A survey on deep learning based face recognition[J]. Computer Vision and Image Understanding, 189, 102805(2019).

[119] Bai X F, Gao N, Zhang Z H et al. 3D palmprint identification combining blocked ST and PCA[J]. Pattern Recognition Letters, 100, 89-95(2017).

[120] Wang X, Gai S Y, Da F P. Fusion of geometric and orientation information for 3D palmprint recognition[J]. Journal of Graphics, 41, 390-398(2020).

[121] Feng S J, Zuo C, Zhang L et al. Generalized framework for non-sinusoidal fringe analysis using deep learning[J]. Photonics Research, 9, 1084-1098(2021).

[122] Qian J M, Feng S J, Li Y X et al. Single-shot absolute 3D shape measurement with deep-learning-based color fringe projection profilometry[J]. Optics Letters, 45, 1842-1845(2020).

[123] Zhang L, Chen Q, Zuo C et al. High-speed high dynamic range 3D shape measurement based on deep learning[J]. Optics and Lasers in Engineering, 134, 106245(2020).